Algebra Algebra Please wait while the activity loads. If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled. If loading fails, click here to try again Question 1 Given two numbers x and y such that 1. x3 + y3 = 9 2. x + y = 3 Find the value of x4+y4 2/3 7 13 17 Algebra Discuss itQuestion 1-Explanation: x3+y3 = (x + y) × (x2 − xy + y2) Putting given values of x3+y3 and (x + y) 9 = 3 × ((x+y)2 − 3xy) = 3 × (9 − 3xy) = 27 − 9xy 9xy = 18 xy = 2 x4 + y4 = (x2 + y2)2 - 2x2y2 = (x2 + y2)2 - 2*4 [Putting value of xy] = ((x + y)2 - 2xy)2 - 2*4 [Putting values of (x+y) and xy] = (9 - 4)2 - 2*4 = 17Question 2 The value of x+1/2x is given as 2, then find the value of 8x3+1/x3 40/3 20/7 28 40 Algebra Discuss itQuestion 2-Explanation: x3 + 1/8x3 + 3.x.1/2x(x + 1/2x) = (x+1/2x)3 x3 + 1/8x3 + 3 = 23 x3 + 1/8x3 = 5 8x3 + 1/x3 = 5.8 = 40 Question 3 If x takes only real numbers. For what value of x, the value of the expression: 4−6x−x2 will be maximum? -4 -3 0 3 Algebra Discuss itQuestion 3-Explanation: Differentiate and equate to 0 6+2x =0 x=−3 Question 4 For what value of x, the following equation: 5√x +12√x =13√x will be true? -2 0 3 None of the above Algebra Discuss itQuestion 4-Explanation: say x=117!=13for, x=2 and 3 also not possible x=4 52+122=132 169=169 Question 5 Solve for x in the equation: log(2x - 1) + log(3) = log(x + 5) x = -1/3 x = 1/3 x = 5/3 x = 8/5 Algebra Discuss itQuestion 5-Explanation: Using the property of logarithms that states log(a) + log(b) = log(ab), we can simplify the equation as log(3(2x - 1)) = log(x + 5). Therefore, we have 6x - 3 = x + 5. Simplifying, we get 5x = 8, which gives us x = 8/5. Hence, the answer is D) x = 8/5. Question 6 If the value of b2 + 1⁄b2 = 1, then find the value of b3 + 1⁄b3 -1/12 -2 -4 None of the above Algebra Discuss itQuestion 6-Explanation: E = (b + 1⁄b)(b2 - 1 + 1⁄b2)Question 7 1 + 1/(x+4) x+4 1/x (x+4)/ x Algebra Discuss itQuestion 7-Explanation: Question 8 If a+b+c = 0, then the value of (a^2/bc) + (b^2/ac) + (c^2/ab) will be? 3 2 1 0 Algebra Discuss itQuestion 8-Explanation: Question 9Following instructions are to be used throughout the quiz: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both the statements and Give answer (a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question. (b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question. (c) if the data in each Statement I and Statement II alone is sufficient to answer the question. (d) if the data even in both Statements I and II together are not sufficient to answer the question. (e) if the data in both Statements I and II together are necessary to answer the question. If x,y are integers, then (x2 + y2)1/2 is an integer? I) x2 + y2 is an integer II) x2 - 3y2 = 0ABCDEData Sufficiency Algebra Discuss itQuestion 9-Explanation: Statement 1: x2 + y2 is an integer Since x and y are integer x2+y2 can be any real number which may not be a perfect square so statement 1 alone cant prove whether (x2+y2)(½) is an integer or not. Statement 2: x2- 3y2 = 0 =>x2+y2-4y2=0 =>x2+y2=4y2 => (x2+y2)(½)= 2y Which is an integer because y is an integer. Question 104/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8. What is half of that number?63063315105Algebra Discuss itQuestion 10-Explanation: Let the number be x. Then, 4/15 of 5x/7 = 4/9 of 2x/5 + 8 4/15 * 5x/7 = 4/9 * 2x/5 + 8 4x/21 = 8x/45 + 8 x/21 = 2x/45 + 2 x/21 = (2x + 90)/45 45x = 21(2x + 90) 45x = 42x + 90*21 3x = 90*21 x = 30*21 = 630. Half of the number will be x/2 x/2 = 630/2 = 315. 12 There are 20 questions to complete. You have completed questions question Your accuracy is Correct Wrong Partial-Credit You have not finished your quiz. If you leave this page, your progress will be lost. Correct Answer You Selected Not Attempted Final Score on Quiz Attempted Questions Correct Attempted Questions Wrong Questions Not Attempted Total Questions on Quiz Question Details Results Date Score Hint Time allowed minutes seconds Time used Answer Choice(s) Selected Question Text Need more practice! Keep trying! Not bad! Good work! Perfect! Last Updated : 27 Sep, 2023 Share your thoughts in the comments Add Your Comment Please Login to comment...